From my limited research into ethical hacking, it seems white hat refers to those who only hack into systems after receiving permission from the owner of the system. They try to penetrate the security measures in place, and then work with the owner of the system to beef up the security.
Black hat hackers, are evil scum who hack into systems to steal information, install ransom ware, wreak havoc, etc. Their intent is to do harm to the target, not help anyone (except themselves).
Grey hat hackers may have intentions to help secure a system or network, but don’t get permission before hacking the system. They might hack a system, and then inform the owner how vulnerable they are, and use the fact that their system is vulnerable to convince the owner that they should pay for the hacker’s services. They use illegal measures to possibly do some good in the end.
In my opinion, grey and black should be clearly avoided. White hat hackers provide a valuable service. Black hat is just plain wrong, and grey hat amounts to extortion at best.
Good luck on your journey!